1. Field of the Invention
This invention relates to signal transmission and reception using information modulation of a chaotic carrier, and in particular to secure communication using a modulated chaotic carrier transmitted over a conventional communication link.
2. Description Relative to the Prior Art
By modulating a chaotic carrier with an information signal whose frequency components lie within the same band as the components of the chaotic carrier, the chaotic nature of the resultant signal masks the presence of the information being transmitted. Analysis of the signal by conventional data evaluation means commonly used in the art, such as Fourier analysis, will neither lead to recovery of the information itself, nor provide confirmation that information is, in fact, being transmitted over the channel. Attendantly, communication over the chaotic channel is highly secure.
To provide such a secure channel, systems for the modulation of a chaotic carrier by an information signal have been disclosed in technical journal articles and in recently issued patents. Generally, the apparatus disclosed consists of a non-linear transmitter adjusted to generate chaotic oscillations which are characterized by local instability of its trajectories in the multi-dimensional phase space of the generator. This instability provides noise like oscillations which have a continuous, broad band frequency spectrum. The spectrum of the carrier can be controlled by variation of the parameters of the generator, and the modulation is effected by mixing the information signal with the chaotic signal of the generator.
At the receiving site, the modulated chaotic carrier is applied to the input of a receiver containing a circuit which replicates the circuit of the chaotic generator of the transmitter. The received modulated chaotic carrier forces the receiver circuit to oscillate with chaotic trajectories identical to those of the transmitting generator, locally reproducing a demodulating signal which is synchronous with the received carrier. The locally reproduced chaotic oscillation is then subtracted from the received modulated carrier to recover the original information signal.
Among prior art disclosures of interest are U.S. Pat. No. 5,291,555 issued to Cuomo et al, U.S. Pat. No. 5,379,346 issued to Pecora et al, and an article published in the journal "Technical Physics Letters", 19(2), February 1993 entitled "Synchronous Chaotic Response of a Nonlinear Oscillator System as a Principle for the Detection of the Information Component of Chaos" by A. R. Volkovskii and N. F. Rul'kov, which disclose various circuits that implement the above described technique. The modulation methods described in these references utilize conventional analog mixing of the chaotic carrier by the information signal, with correspondingly conventional demodulation. In these disclosures, in order to deter an eavesdropper a low amplitude information signal must be used, leading to a loss in signal to noise ratio and to a relative ease of breaking the secure communication, as is pointed out in the article "Steps Toward Unmasking Secure Communications", International Journal of Bifurcation and Chaos in Applied Science and Engineering, August 1994, 4(4).
The use of filters in chaotic systems which serve only to suppress large "spike" components at specific frequencies has been disclosed in U.S. Pat. No. 5,291,555 issued to Cuomo et al, mentioned above, and in the article "Using Filters for Chaotic Synchronization for Communications", by T. L. Carroll, IEEE International Symposium for Circuits and Systems, April 1995, Seattle, Wash.
A discussion of the digital implementation of chaotic covert communication is presented in an article "Chaotic Digital Encoding: an Approach to Secure Communication" by D. R. Frey IEEE Transactions on Circuits and Systems-II. Analog and Digital Signal Processing, 40(10) 1993. In Frey's paper, a chaotic modulator and demodulator implemented by means of a non-linear digital filter consisting of shift registers is disclosed.
It will be noted that the above prior art does not address the effect of the band limited characteristics of real world transmission links. The frequency bandwidth of available links typically lack low frequency response with an inability to transmit dc signals, and have a high frequency cutoff defining the upper end of the band. Resultantly, a transmission link has a band pass characterized by certain frequency and phase particularities, and these important real world characteristics are not addressed in the chaotic covert communication systems disclosed in the prior art. In the teaching of the present invention, transmission link bandwidth limitations are considered, and are dealt with in the overall design of the chaotic covert communication system.